Quantizing the Moduli Space of Parabolic Higgs Bundles

Abstract

We consider the moduli space \( M_H^S \) of stable parabolic Higgs bundles (of rank 2 for simplicity) over a compact Riemann surface of genus g > 1. This is a smooth variety over ℂ, equipped with a holomorphic symplectic form \( \Omega _H \) . Any symplectic form is known to admit a quantization, but in general the quantization is not unique. We fix a projective structure P on X. Using P we show that there is a canonical quantization of \( {\Omega _H} \) on a certain Zariski open dense subset \( u \subset M_H^S \), once a projective structure P on X has been specified.